Find the greatest common factor of $175$ and $25$.
Explanation: The greatest common factor (GCF) is the largest number that is a factor of both $175$ and $25$. In order to find the GCF, we can factor each number completely as a product of prime numbers: $ \begin{aligned}175 &=5\cdot5\cdot7\\\\\\\\ 25&=5\cdot5 \end{aligned}$ Now, let's find the factors that are common to each number: $ \begin{aligned}175 &=5\cdot5\cdot7\\\\\\\\ 25&=5\cdot5 \end{aligned}$ Each number shares the factors ${5}$ and ${5}$, so the GCF is $5\cdot5={25}$. The greatest common factor of $175$ and $25$ is $25$.